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NeX [460]
3 years ago
8

The Hernandez family has six

Mathematics
1 answer:
Charra [1.4K]3 years ago
4 0

Answer:10%

Step-by-step explanation:

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What are the signs of the x- and y-coordinates of points within each of the four quadrants in the coordinate plane?
Naily [24]
In the first quadrant the signs would be (x,y) in the second quadrant they would be (-x,y) in the third (-x,-y) and the fourth (x,-y)
5 0
2 years ago
3. The curve C with equation y=f(x) is such that, dy/dx = 3x^2 + 4x +k
Andreas93 [3]

a. Given that y = f(x) and f(0) = -2, by the fundamental theorem of calculus we have

\displaystyle \frac{dy}{dx} = 3x^2 + 4x + k \implies y = f(0) + \int_0^x (3t^2+4t+k) \, dt

Evaluate the integral to solve for y :

\displaystyle y = -2 + \int_0^x (3t^2+4t+k) \, dt

\displaystyle y = -2 + (t^3+2t^2+kt)\bigg|_0^x

\displaystyle y = x^3+2x^2+kx - 2

Use the other known value, f(2) = 18, to solve for k :

18 = 2^3 + 2\times2^2+2k - 2 \implies \boxed{k = 2}

Then the curve C has equation

\boxed{y = x^3 + 2x^2 + 2x - 2}

b. Any tangent to the curve C at a point (a, f(a)) has slope equal to the derivative of y at that point:

\dfrac{dy}{dx}\bigg|_{x=a} = 3a^2 + 4a + 2

The slope of the given tangent line y=x-2 is 1. Solve for a :

3a^2 + 4a + 2 = 1 \implies 3a^2 + 4a + 1 = (3a+1)(a+1)=0 \implies a = -\dfrac13 \text{ or }a = -1

so we know there exists a tangent to C with slope 1. When x = -1/3, we have y = f(-1/3) = -67/27; when x = -1, we have y = f(-1) = -3. This means the tangent line must meet C at either (-1/3, -67/27) or (-1, -3).

Decide which of these points is correct:

x - 2 = x^3 + 2x^2 + 2x - 2 \implies x^3 + 2x^2 + x = x(x+1)^2=0 \implies x=0 \text{ or } x = -1

So, the point of contact between the tangent line and C is (-1, -3).

7 0
2 years ago
PLZ RESPOND AS SOON AS POSSIBLE
lyudmila [28]

the coordinates of point f is B)7,-5

7 0
3 years ago
Help ASAP.
dlinn [17]

24.5 \div 24.5
try that then times it by 12.1
7 0
2 years ago
Read 2 more answers
In a equation below, for what value of c does x=4? 1/2(2x+4)=3x-c
oksano4ka [1.4K]

Answer:

c = 6

Step-by-step explanation:

1/2 (2(4) + 4) = 3(4) - c

1/2 (8 + 4) = 12 - c

1/2 (12) = 12 - c

6 = 12 - c

-6 = -c

c = 6  

5 0
2 years ago
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